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To manage water resources and forecast river flows, hydrologists seek to understand how water moves from precipitation, through watersheds, into river channels. However, we lack fundamental information on the spatial distribution and physical controls on global hydrologic processes. This information is needed to provide theoretical support for large-domain model simulations. Here, to address this issue, we present a global, searchable database of 400 research watersheds with published descriptions of dominant hydrologic flow pathways. This knowledge synthesis approach leverages decades of grant funding, fieldwork effort and local expertise. We use the database to test longstanding hypotheses about the roles of climate, biomes and landforms in controlling hydrologic processes. We show that aridity predicts the depth of water flow pathways and that terrain and biomes predict the prevalence of lateral flow pathways. These new data and search capabilities support efficient hypothesis testing to investigate emergent patterns that relate landscape organization to hydrologic function. 

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology. 

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

Abstract Global gridded precipitation products have proven essential for many applications ranging from hydrological modeling and climate model validation to natural hazard risk assessment. They provide a global picture of how precipitation varies across time and space, specifically in regions where ground-based observations are scarce. While the application of global precipitation products has become widespread, there is limited knowledge on how well these products represent the magnitude and frequency of extreme precipitation—the key features in triggering flood hazards. Here, five global precipitation datasets (MSWEP, CFSR, CPC, PERSIANN-CDR, and WFDEI) are compared to each other and to surface observations. The spatial variability of relatively high precipitation events (tail heaviness) and the resulting discrepancy among datasets in the predicted precipitation return levels were evaluated for the time period 1979–2017. The analysis shows that 1) these products do not provide a consistent representation of the behavior of extremes as quantified by the tail heaviness, 2) there is strong spatial variability in the tail index, 3) the spatial patterns of the tail heaviness generally match the Köppen–Geiger climate classification, and 4) the predicted return levels for 100 and 1000 years differ significantly among the gridded products. More generally, our findings reveal shortcomings of global precipitation products in representing extremes and highlight that there is no single global product that performs best for all regions and climates. 

Abstract Surface meteorological analyses are an essential input (termed “forcing”) for hydrologic modeling. This study investigated the sensitivity of different hydrologic model configurations to temporal variations of seven forcing variables (precipitation rate, air temperature, longwave radiation, specific humidity, shortwave radiation, wind speed, and air pressure). Specifically, the effects of temporally aggregating hourly forcings to hourly daily average forcings were examined. The analysis was based on 14 hydrological outputs from the Structure for Unifying Multiple Modeling Alternatives (SUMMA) model for the 671 Catchment Attributes and Meteorology for Large-Sample Studies (CAMELS) basins across the contiguous United States (CONUS). Results demonstrated that the hydrologic model sensitivity to temporally aggregating the forcing inputs varies across model output variables and model locations. We used Latin hypercube sampling to sample model parameters from eight combinations of three influential model physics choices (three model decisions with two options for each decision, i.e., eight model configurations). Results showed that the choice of model physics can change the relative influence of forcing on model outputs and the forcing importance may not be dependent on the parameter space. This allows for model output sensitivity to forcing aggregation to be tested prior to parameter calibration. More generally, this work provides a comprehensive analysis of the dependence of modeled outcomes on input forcing behavior, providing insight into the regional variability of forcing variable dominance on modeled outputs across CONUS. 

Abstract As droughts have widespread social and ecological impacts, it is critical to develop long‐term adaptation and mitigation strategies to reduce drought vulnerability. Climate models are important in quantifying drought changes. Here, we assess the ability of 285 CMIP6 historical simulations, from 17 models, to reproduce drought duration and severity in three observational data sets using the Standardized Precipitation Index (SPI). We used summary statistics beyond the mean and standard deviation, and devised a novel probabilistic framework, based on the Hellinger distance, to quantify the difference between observed and simulated drought characteristics. Results show that many simulations have less thanerror in reproducing the observed drought summary statistics. The hypothesis that simulations and observations are described by the same distribution cannot be rejected for more thanof the grids based on ourdistance framework. No single model stood out as demonstrating consistently better performance over large regions of the globe. The variance in drought statistics among the simulations is higher in the tropics compared to other latitudinal zones. Though the models capture the characteristics of dry spells well, there is considerable bias in low precipitation values. Good model performance in terms of SPI does not imply good performance in simulating low precipitation. Our study emphasizes the need to probabilistically evaluate climate model simulations in order to both pinpoint model weaknesses and identify a subset of best‐performing models that are useful for impact assessments.